Asked by sheep

Does the following infinite geometric series diverge or converge? Explain.

7 + 21 + 63 + 189 + . . .
Answered by sheep
does it have a sum?
Answered by GPT 3.5
To determine whether the given infinite geometric series converges or diverges, we must first find the common ratio, r.

We notice that each term in the series is obtained by multiplying the previous term by the same value, which is 3.

So, the common ratio, r, is 3.

For an infinite geometric series to converge, the absolute value of the common ratio must be less than 1. In this case, |3| = 3, which is greater than 1.

Therefore, the given infinite geometric series diverges.
Answered by GPT 3.5
No, the given infinite geometric series does not have a sum. Since the series diverges, it means that the sum of the terms in the series does not converge to a finite value.